%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO044-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:16:53 AM UTC 2026
% Result : Unsatisfiable 0.13s 10.97s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 61 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 73 ( 14 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(segment_construction1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : between(VAR_0,VAR_1,extension(VAR_0,VAR_1,VAR_2,VAR_3)),
file('theBenchmark.p',segment_construction1) ).
cnf(c_4,plain,
between(A,B,extension(A,B,C,D)),
inference(clausify,[status(thm)],[segment_construction1]) ).
fof(segment_construction2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : equidistant(VAR_0,extension(VAR_1,VAR_0,VAR_2,VAR_3),VAR_2,VAR_3),
file('theBenchmark.p',segment_construction2) ).
cnf(c_5,plain,
equidistant(A,extension(B,A,C,D),C,D),
inference(clausify,[status(thm)],[segment_construction2]) ).
fof(d4_4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( equidistant(VAR_3,VAR_2,VAR_0,VAR_1)
| ~ equidistant(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',d4_4) ).
cnf(c_26,plain,
( equidistant(D,C,A,B)
| ~ equidistant(A,B,C,D) ),
inference(clausify,[status(thm)],[d4_4]) ).
fof(b0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( between(VAR_1,VAR_2,VAR_0)
| VAR_0 != extension(VAR_1,VAR_2,VAR_3,VAR_4) ),
file('theBenchmark.p',b0) ).
cnf(c_31,plain,
( between(B,C,A)
| A != extension(B,C,D,E) ),
inference(clausify,[status(thm)],[b0]) ).
cnf(c_32,plain,
( between(A,B,E)
| extension(A,B,C,D) != E ),
inference(copy,[status(thm)],[c_31]) ).
fof(d9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| VAR_0 = VAR_1
| ~ equidistant(VAR_1,VAR_2,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',d9) ).
cnf(c_42,plain,
( C = D
| A = B
| ~ equidistant(B,C,B,D)
| ~ between(A,B,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[d9]) ).
fof(b5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( between(VAR_1,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_2,VAR_3)
| ~ between(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',b5) ).
cnf(c_58,plain,
( between(B,C,D)
| ~ between(A,C,D)
| ~ between(A,B,C) ),
inference(clausify,[status(thm)],[b5]) ).
fof(v_between_u_and_w,axiom,
between(u,v,w),
file('theBenchmark.p',v_between_u_and_w) ).
cnf(c_59,plain,
between(u,v,w),
inference(clausify,[status(thm)],[v_between_u_and_w]) ).
fof(w_between_v_and_x,axiom,
between(v,w,x),
file('theBenchmark.p',w_between_v_and_x) ).
cnf(c_60,plain,
between(v,w,x),
inference(clausify,[status(thm)],[w_between_v_and_x]) ).
fof(v_not_w,axiom,
v != w,
file('theBenchmark.p',v_not_w) ).
cnf(c_61,plain,
v != w,
inference(clausify,[status(thm)],[v_not_w]) ).
cnf(c_62,plain,
w != v,
inference(copy,[status(thm)],[c_61]) ).
fof(prove_w_between_u_and_x,axiom,
~ between(u,w,x),
file('theBenchmark.p',prove_w_between_u_and_x) ).
cnf(c_63,plain,
~ between(u,w,x),
inference(clausify,[status(thm)],[prove_w_between_u_and_x]) ).
cnf(c_133,plain,
equidistant(A,B,C,extension(D,C,B,A)),
inference(resolve,[status(thm)],[c_26,c_5]) ).
cnf(c_215,plain,
( between(v,w,A)
| ~ between(u,w,A) ),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_729,plain,
( x = A
| v = w
| ~ equidistant(w,x,w,A)
| ~ between(v,w,A) ),
inference(resolve,[status(thm)],[c_60,c_42]) ).
cnf(c_730,plain,
( x = A
| w = v
| ~ equidistant(w,x,w,A)
| ~ between(v,w,A) ),
inference(copy,[status(thm)],[c_729]) ).
cnf(c_249,plain,
( x = A
| ~ equidistant(w,x,w,A)
| ~ between(v,w,A) ),
inference(resolve,[status(thm)],[c_62,c_730]) ).
cnf(c_282,plain,
extension(u,w,A,B) != x,
inference(resolve,[status(thm)],[c_32,c_63]) ).
cnf(c_439,plain,
between(v,w,extension(u,w,A,B)),
inference(resolve,[status(thm)],[c_215,c_4]) ).
cnf(c_731,plain,
( x = extension(u,w,A,B)
| ~ equidistant(w,x,w,extension(u,w,A,B)) ),
inference(resolve,[status(thm)],[c_439,c_249]) ).
cnf(c_732,plain,
( extension(u,w,A,B) = x
| ~ equidistant(w,x,w,extension(u,w,A,B)) ),
inference(copy,[status(thm)],[c_731]) ).
cnf(c_727,plain,
~ equidistant(w,x,w,extension(u,w,A,B)),
inference(resolve,[status(thm)],[c_282,c_732]) ).
cnf(c_728,plain,
$false,
inference(resolve,[status(thm)],[c_727,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO044-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.60 % Computer : n013.cluster.edu
% 0.09/10.60 % Model : x86_64 x86_64
% 0.09/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.60 % Memory : 8046.5625MB
% 0.09/10.60 % OS : Linux 6.8.0-71-generic
% 0.09/10.60 % CPULimit : 300
% 0.09/10.60 % WCLimit : 300
% 0.09/10.60 % DateTime : Fri Sep 25 12:34:48 UTC 2026
% 0.09/10.60 % CPUTime :
% 0.09/10.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.60 % Process 434277 was started by sandbox on n013,
% 0.09/10.60 % Fri Sep 25 12:34:48 2026
% 0.09/10.60 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.61
% 0.09/10.61 % From the command line: assign(max_seconds, 300).
% 0.13/10.97
% 0.13/10.97 % SZS status Unsatisfiable for theBenchmark
% 0.13/10.97
% 0.13/10.97 % Proof 1 at 0.33 (+ 0.02) seconds.
% 0.13/10.97 % Length of proof is 19.
% 0.13/10.97 % Level of proof is 4.
% 0.13/10.97 % Maximum clause weight is 24.000.
% 0.13/10.97 % Given clauses 152.
% 0.13/10.97
% 0.13/10.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------